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arXiv · 1710.11433

Statistical properties of eigenstate amplitudes in complex quantum systems

Wouter Beugeling·Arnd Bäcker·Roderich Moessner·Masudul Haque
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Abstract

We study the eigenstates of quantum systems with large Hilbert spaces, via their distribution of wavefunction amplitudes in a real-space basis. For single-particle 'quantum billiards', these real-space amplitudes are known to have Gaussian distribution for chaotic systems. In this work, we formulate and address the corresponding question for many-body lattice quantum systems. For integrable many-body systems, we examine the deviation from Gaussianity and provide evidence that the distribution generically tends toward power-law behavior in the limit of large sizes. We relate the deviation from Gaussianity to the entanglement content of many-body eigenstates. For integrable billiards, we find several cases where the distribution has power-law tails.

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Wouter Beugeling, Arnd Bäcker, Roderich Moessner, Masudul Haque. 2017-10-31. Statistical properties of eigenstate amplitudes in complex quantum systems. https://doi.org/10.1103/physreve.98.022204

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